A dielectric has a time constant for redistribution of charge
that is given by τD = ε/σ(E), where ε is the absolute dielectric
constant (about 20 × 10–12 F/m for XLPE) and σ(E) is the fielddependent
conductivity. For the charge distribution to limit the
electric field, this time constant must be comparable with the
time constant for the change of the voltage, i.e., τD = τV = ωV
-1.
Thus, we have
ε 1
= tv
= or σ(Elim) = εω (1)
σ(Elim) ωv
where ω is the applied frequency of the AC voltage, and σ(Elim) is
the conductivity at the space charge limited field, Elim, in the region
of the defect tip. Thus, for such a system when the applied
voltage is sufficiently large, we expect a region of constant electric
field (Elim) near the tip of the defect with a decreasing field